Solve 200=pi*r^2

$$200 = \pi \times r ^ { 2 }$$

Solve for r

$$r=10\sqrt{\frac{2}{\pi }}\approx 7.978845608$$

$$r=-10\sqrt{\frac{2}{\pi }}\approx -7.978845608$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$\pi r^{2}=200$$

Divide both sides by \pi .

$$\frac{\pi r^{2}}{\pi }=\frac{200}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$r^{2}=\frac{200}{\pi }$$

Take the square root of both sides of the equation.

$$r=\frac{20}{\sqrt{2\pi }} r=-\frac{20}{\sqrt{2\pi }}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$\pi r^{2}=200$$

Subtract 200 from both sides.

$$\pi r^{2}-200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\pi \left(-200\right)}}{2\pi }$$

Square 0.

$$r=\frac{0±\sqrt{-4\pi \left(-200\right)}}{2\pi }$$

Multiply -4 times \pi .

$$r=\frac{0±\sqrt{\left(-4\pi \right)\left(-200\right)}}{2\pi }$$

Multiply -4\pi times -200.

$$r=\frac{0±\sqrt{800\pi }}{2\pi }$$

Take the square root of 800\pi .

$$r=\frac{0±20\sqrt{2\pi }}{2\pi }$$

Now solve the equation r=\frac{0±20\sqrt{2\pi }}{2\pi } when ± is plus.

$$r=\frac{20}{\sqrt{2\pi }}$$

Now solve the equation r=\frac{0±20\sqrt{2\pi }}{2\pi } when ± is minus.

$$r=-\frac{20}{\sqrt{2\pi }}$$

The equation is now solved.

$$r=\frac{20}{\sqrt{2\pi }} r=-\frac{20}{\sqrt{2\pi }}$$